I'm not sure what's normal when you buy tayberries as I got one in a pot that had been rooted off one a member of my family already had. However, I planted it up and trained all the shoots on a series of wires to the right. The following year those shoots fruited and I cut them back. Meanwhile new shoots were trained to the left for fruiting the following year. There's some good advice about training on the Ken Muir site under the Ask Ken section but, unless they have already fruited then I'd not cut them down at all.

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Some of us live in the past, always talking about back then. Some of us live in the future, always planning what we are going to do. And, then there are those, who neither look behind or ahead, but just enjoy the moment of right now.

Which one are you and is it how you want to be?